This study investigated the solubility of benzenesulfonamide (BSA) as a model compound using experimental and computational methods. New experimental solubility data were collected in the solvents DMSO, DMF, 4FM, and their binary mixtures with water. The predictive model was constructed based on the best-performing regression models trained on available experimental data, and their hyperparameters were optimized using a newly developed Python code. To evaluate the models, a novel scoring function was formulated, considering not only the accuracy but also the bias–variance tradeoff through a learning curve analysis. An ensemble approach was adopted by selecting the top-performing regression models for test and validation subsets. The obtained model accurately back-calculated the experimental data and was used to predict the solubility of BSA in 2067 potential solvents. The analysis of the entire solvent space focused on the identification of solvents with high solubility, a low environmental impact, and affordability, leading to a refined list of potential candidates that meet all three requirements. The proposed procedure has general applicability and can significantly improve the quality and speed of experimental solvent screening.